Summary: Sample solutions for Problem 5 in Problem Set 13 with
Macaulay2
Chris Peterson and Hirotachi Abo
Problem 5 (Set 13). Let k be an algebraically closed field, let F = y2
-x3
-x2
and G = (x2
+ y2
)2
+ 3x2
y - y3
be polynomials in R := k[x, y], and let C1
and C2 denote the curves V (F) and V (G) in A2
respectively. Then the point
P = (0, 0) is contained in both C1 and C2. We compute the intersection
number of I(P, F G). Recall that I(P, F G) is defined to be the following
vector space
dimk(OP (A2
)/(F, G)OP (A2
)),

Source: Abo, Hirotachi - Department of Mathematics, University of Idaho

Collections: Mathematics